In this paper we study the electromagnetic scattering, absorption, and performance bounds for short time modulated pulses that impinge on a time-varying lossy layer that is sandwiched between vacuum and a perfect electric conductor. The electric characteristics of the layer, namely, the conductivity, permittivity, and permeability, are assumed to change abruptly or gradually in time. We demonstrate numerically that a time-varying absorbing layer that undergoes temporal switching of its permittivity and conductance can absorb the power of a modulated, ultrawideband, as well as a quasimonochromatic, pulsed wave beyond what is dictated by the time-invariant Rozanov bound when integrating over the whole frequency spectrum. We suggest and simulate a practical metamaterial realization that is constructed as a three-dimensional array of resistor loaded dipoles. By switching only the dipole’s load resistance, desired effective media properties are obtained. Furthermore, we show that Rozanov’s bound can be bypassed with abrupt and a more practical gradual, soft, switching, thus overcoming some possible causality issues in abrupt switching.